## On the $W$-action on $B$-sheets in positive characteristic

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- by Friedrich Knop and Guido Pezzini PDF
- Represent. Theory
**19**(2015), 9-23 Request permission

## Abstract:

Let $G$ be a connected reductive group defined over an algebraically closed base field of characteristic $p\ge 0$, let $B\subseteq G$ be a Borel subgroup, and let $X$ be a $G$-variety. We denote the (finite) set of closed $B$-invariant irreducible subvarieties of $X$ that are of maximal complexity by $\mathfrak {B}_{0}(X)$. The first named author has shown that for $p=0$ there is a natural action of the Weyl group $W$ on $\mathfrak {B}_{0}(X)$ and conjectured that the same construction yields a $W$-action whenever $p\ne 2$. In the present paper, we prove this conjecture.## References

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## Additional Information

**Friedrich Knop**- Affiliation: Department Mathematik, FAU Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
- MR Author ID: 103390
- ORCID: 0000-0002-4908-4060
**Guido Pezzini**- Affiliation: Department Mathematik, FAU Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
- MR Author ID: 772887
- Received by editor(s): September 2, 2013
- Received by editor(s) in revised form: November 10, 2014, and February 3, 2015
- Published electronically: March 6, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Represent. Theory
**19**(2015), 9-23 - MSC (2010): Primary 20G15, 14M17, 14L30, 20G05
- DOI: https://doi.org/10.1090/S1088-4165-2015-00464-9
- MathSciNet review: 3318502